Undergraduate Programme and Module Handbook 2023-2024

# Module MATH2071: MATHEMATICAL PHYSICS II

## Department: Mathematical Sciences

### MATH2071: MATHEMATICAL PHYSICS II

Type | Open | Level | 2 | Credits | 20 | Availability | Available in 2023/24 | Module Cap | Location | Durham |
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#### Prerequisites

- Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) AND Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071) AND [Dynamics 1 (MATH1607) OR Foundations of Physics I (PHYS1122)] [the latter two modules may be a co-requisite]

#### Corequisites

- Dynamics 1 (MATH1607) unless taken before, or unless Foundations of Physics I (PHYS1122) has been taken before.

#### Excluded Combination of Modules

- Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571), Theoretical Physics 2 (PHYS2631)

#### Aims

- To appreciate the conceptual framework of classical and quantum physics.

#### Content

- Lagrangian and Hamiltonian Dynamics.
- The Wave Equation
- Small oscillations of systems of particles.
- Physics basis of Quantum Mechanics,
- Schrodingers Equation

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Mathematical Physics.
- have an awareness of the abstract concepts of theoretical mathematics in the field of Mathematical Physics.
- have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas:
- Lagrangian and Hamiltonian Dynamics.
- Symmetries and their relation to conserved quantities.
- Small oscillations of systems of particles.
- Wave equations.
- Elementary Quantum Mechanics.
- Wave functions and their probabilistic interpretation.
- Applications to simple physical problems.

Subject-specific Skills:

- In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Modelling.

Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
- Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
- Tutorials provide active engagement and feedback to the learning process.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week | 1 Hour | 42 | |

Tutorials | 10 | Fortnightly for 21 weeks | 1 Hour | 10 | ■ |

Problems Classes | 9 | Fortnightly for 20 weeks | 1 Hour | 9 | |

Preparation and Reading | 139 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 hours | 100% | Yes |

#### Formative Assessment:

Fortnightly or weekly written assignments in the first 2 terms.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University